TSTP Solution File: SYO889^16 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYO889^16 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 08:58:42 EDT 2024
% Result : Theorem 3.12s 1.75s
% Output : Refutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 25
% Syntax : Number of formulae : 32 ( 12 unt; 13 typ; 7 def)
% Number of atoms : 82 ( 7 equ; 0 cnn)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 145 ( 2 ~; 0 |; 15 &; 117 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 52 ( 21 ^ 21 !; 10 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mrel_type,type,
mrel: mworld > mworld > $o ).
thf(mactual_type,type,
mactual: mworld ).
thf(mlocal_type,type,
mlocal: ( mworld > $o ) > $o ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mand_type,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mand_def,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(mimplies_type,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(mbox_type,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: mworld > $o,B: mworld] :
! [C: mworld] :
( ( mrel @ B @ C )
=> ( A @ C ) ) ) ) ).
thf(mdia_type,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(mdia_def,definition,
( mdia
= ( ^ [A: mworld > $o,B: mworld] :
? [C: mworld] :
( ( mrel @ B @ C )
& ( A @ C ) ) ) ) ).
thf(eiw_di_type,type,
eiw_di: $i > mworld > $o ).
thf(mforall_di_type,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(mforall_di_def,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
! [C: $i] :
( ( eiw_di @ C @ B )
=> ( A @ C @ B ) ) ) ) ).
thf(mexists_di_type,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(mexists_di_def,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
? [C: $i] :
( ( eiw_di @ C @ B )
& ( A @ C @ B ) ) ) ) ).
thf(a_type,type,
a: $i > mworld > $o ).
thf(b_type,type,
b: $i > mworld > $o ).
thf(5,axiom,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_nonempty) ).
thf(21,plain,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: mworld] : ( mrel @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(17,plain,
! [A: mworld] : ( mrel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
( mlocal
@ ( mimplies
@ ( mand
@ ( mdia
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( a @ A ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mdia @ ( b @ A ) ) ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [A: $i] : ( mdia @ ( mand @ ( a @ A ) @ ( b @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mand
@ ( mdia
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( a @ A ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mdia @ ( b @ A ) ) ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [A: $i] : ( mdia @ ( mand @ ( a @ A ) @ ( b @ A ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( ( ? [A: mworld] :
( ( mrel @ mactual @ A )
& ? [B: $i] :
( ( eiw_di @ B @ A )
& ! [C: mworld] :
( ( mrel @ A @ C )
=> ( a @ B @ C ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ? [C: mworld] :
( ( mrel @ A @ C )
& ( b @ B @ C ) ) ) ) )
=> ? [A: mworld] :
( ( mrel @ mactual @ A )
& ? [B: $i] :
( ( eiw_di @ B @ A )
& ? [C: mworld] :
( ( mrel @ A @ C )
& ( a @ B @ C )
& ( b @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: mworld,B: mworld,C: $i] :
( ( ( eiw_di @ C @ A )
& ( mrel @ A @ B ) )
=> ( eiw_di @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_cumul) ).
thf(23,plain,
! [A: mworld,B: mworld,C: $i] :
( ( ( eiw_di @ C @ A )
& ( mrel @ A @ B ) )
=> ( eiw_di @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ A @ B )
& ( mrel @ B @ C ) )
=> ( mrel @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_transitive) ).
thf(19,plain,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ A @ B )
& ( mrel @ B @ C ) )
=> ( mrel @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,plain,
$false,
inference(e,[status(thm)],[21,17,7,23,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYO889^16 : TPTP v8.2.0. Released v8.1.0.
% 0.16/0.16 % Command : run_Leo-III %s %d
% 0.16/0.38 % Computer : n012.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Mon May 20 08:39:24 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.95/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.02 % [INFO] Parsing done (124ms).
% 1.27/1.03 % [INFO] Running in sequential loop mode.
% 1.80/1.26 % [INFO] eprover registered as external prover.
% 1.80/1.26 % [INFO] cvc4 registered as external prover.
% 1.80/1.26 % [INFO] Scanning for conjecture ...
% 2.04/1.34 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.12/1.36 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.12/1.37 % [INFO] Problem is higher-order (TPTP THF).
% 2.12/1.37 % [INFO] Type checking passed.
% 2.12/1.38 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.12/1.75 % External prover 'e' found a proof!
% 3.12/1.75 % [INFO] Killing All external provers ...
% 3.12/1.75 % Time passed: 1210ms (effective reasoning time: 720ms)
% 3.12/1.75 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.12/1.75 % Axioms used in derivation (4): eiw_di_nonempty, mrel_reflexive, eiw_di_cumul, mrel_transitive
% 3.12/1.75 % No. of inferences in proof: 12
% 3.12/1.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1210 ms resp. 720 ms w/o parsing
% 3.32/1.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.32/1.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------